Class 11 Mathematics Probability MCQs Set 03

Question. A coin is tossed 3 times, the probability of getting exactly two heads is m/8 . The value of ‘m’ is
(a) 1
(b) 2
(c) 3
(d) 4

Answer: C

Question. If A, B and C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B) = P(C), then P(A) is equal to …
(a) 1/11
(b) 2/11
(c) 5/11
(d) 6/11

Answer: B

Question. If 2/11 is the probability of an event, then the probability of the event ‘not A’, is
(a) 9/11
(b) 11/2
(c) 11/9
(d) 2/11

Answer: A

Question. If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails as
(a) > . 5
(b) 0.5
(c) ≤.5
(d) 0

Answer: C

Question. The probability that a randomly chosen two-digit positive integer is a multiple of 3, is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/5

Answer: B

Question. In a school there are 40% science students and the remaining 60% are arts students. It is known that 5% of the science students are girls and 10% of the arts students are girls. One student selected at random is a girl. What is the probability that she is an arts student?
(a) 1/3
(b) 3/4
(c) 1/5
(d) 3/5

Answer: B

Question. Two dice are thrown simultaneously. The probability of obtaining a total score of seven is 1/m . The value of ‘m’ is
(a) 3
(b) 2
(c) 6
(d) 9

Answer: C

Question. A fair die is thrown once. The probability of getting a composite number less than 5 is
(a) 1/3
(b) 1/6
(c) 2/3
(d) 0

Answer: B

Question. In a simultaneous throw of 2 coins, the probability of having 2 heads is:
(a) 1/4
(b) 1/2
(c) 1/8
(d) 1/6

Answer: A

Question. The probability of getting sum more than 7 when a pair of dice are thrown is:
(a) 7/36
(b) 5/12
(c) 7/12
(d) None of the options

Answer: B

Question. The probability that a two digit number selected at random will be a multiple of ‘3’ and not a multiple of ‘5’ is
(a) 2/15
(b) 4/15
(c) 1/15
(d) 4/90

Answer: B

Question. If 1+ 4p/2 ,1 − p/2 and 1− 2p/2 are the probabilities of three mutually exclusive events, then value of p is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 2/3

Answer: A

Question. If P(A∪B) = P(A∩B) for any two events A and B, then
(a) P(A) = P(B)
(b) P(A) > P(B)
(c) P(A) < P(B)
(d) None of the options

Answer: A

Question. If an event has more than one sample point, then it is called a/an
(a) simple event
(b) elementary event
(c) compound event
(d) None of the options

Answer: C

Question. Which of the following cannot be the probability of an event?
(a) 2/3
(b) – 1/5
(c) 15%
(d) 0.7

Answer: B

Question. If A and B are two events, then which of the following is true?
(a) P(A∪B) = P(A) + P(B)
(b) P(A∪B) = P(A) + P(B) − ∑P(ωi),∀ωi ∈ A∩B
(c) P(A∪B) = P(A) + P(B) − P(A∩B)
(d) Both (b) and (c)

Answer: D

Question. A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”, Then, E and F are
(a) mutually exclusive
(b) exhaustive
(c) mutually exclusive and exhaustive
(d) None of the options

Answer: D

Question. A coin is tossed once, then the sample space is
(a) {H}
(b) {T}
(c) {H, T}
(d) None of the options

Answer: C

Question. A coin is tossed repeatedly until a tail comes up for the first time. Then, the sample space for this experiment is
(a) {T, HT, HTT}
(b) {TT, TTT, HTT, THH}
(c) {T, HT, HHT, HHHT, HHHHT, …}
(d) None of the options

Answer: C

Question. An experiment is called random experiment, if it
(a) has more than one possible outcome
(b) is not possible to predict the outcome in advance
(c) Both (a) and (b)
(d) None of the options

Answer: C

Question. A die is thrown. The probability of getting a number less than or equal to 6 is
(a) 6
(b) 1
(c) 2
(d) 5

Answer: B

Question. In a leap year, the probability of having 53 Sundays or 53 Mondays is
(a) 2/7
(b) 3/7
(c) 4/7
(d) 5/7

Answer: B

Question. In a leap year the probability of having 53 Sundays or 53 Mondays is
(a) 2/7
(b) 3/7
(c) 4/7
(d) 5/7

Answer: B

Question. Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is
(a) 0.39
(b) 0.25
(c) 0.11
(d) None of the options

Answer: A

STATEMENT TYPE QUESTIONS

Question. A die is thrown.
I. The probability of a prime number will appear is 1/2.
II. The probability of a number more than 6 will appear is 1.
(a) Only I is correct.
(b) Only II is correct.
(c) Both I and II are correct.
(d) Both I and II are incorrect.

Answer: A

Question. A letter is chosen at random from the word ‘ASSASSINATION’.
I. The probability that letter is a vowel is 6/13 .
II. The probability that letter is a consonant is 7/13 .
(a) Only I is correct.
(b) Both I and II are correct.
(c) Only II is correct.
(d) Both are incorrect.

Answer: B

Question. Which of the following is true?
I. If the empty set Φ and the sample space describe events, then Φ ≤is an impossible event.
II. In the above statement, the whole sample space S is called the sure event.
(a) Only I is true
(b) Only II is true
(c) Both I and II are true
(d) Both I and II are false

Answer: C

Question. Consider the following statements.
I. If an event has only one sample point of the sample space is called a simple event.
II. A sample space is the set of all possible outcomes of an experiment.
(a) Only I is true.
(b) Only II is true.
(c) Both I and II are true.
(d) Both I and II are false.

Answer: C

Question. Consider the following statements.
I. If an event has more than one sample point it is called a compound event.
II. A set of events is said to be mutually exclusive if the happening of one excludes the happening of the other i.e. A ∩ B = Φ.
III. An event having no sample point is called null or impossible event.
(a) I and II are true
(b) II and III are true.
(c) I, II and III are true.
(d) None of them are true.

Answer: C

Question. Two dice are thrown. The events A, B and C are as follows:
A : getting an even number on the first die.
B : getting an odd number on the first die.
C : getting the sum of the numbers on the dice ≤ 5. Then,
I. A’ : getting an odd number on the first die
II. A and B = A ∩ B = Φ
III. B and C = B ∩ C = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)}
(a) Only I and II is false.
(b) Only II and III is false.
(c) All I, II and III are false.
(d) All I, II and III are true.

Answer: D

Question. Consider the following statements.
I. P(A or B) = P (A ∪ B) = P(A) + P(B), where A and B are two mutually exclusive events.
II. P(not ‘A’) = 1 – P(A) = P (A) , where P (A) denotes the probability of not happening the event A.
III. P(A ∩ B) = Probability of simultaneous occurrence of A and B.
(a) I, II are true but III is false.
(b) I, III are true but II is false.
(c) II, III are true but I is false.
(d) All three statements are true.

Answer: D